Tokkai10-68315, published by Japan Patent Office in 1998, discloses an exhaust purification device which has a filter or NOx reduction catalyst in the exhaust passage. In order to maintain the filter/catalyst in a suitable temperature region, the temperature of the filter/catalyst is estimated, and the exhaust gas flowrate flowing through the filter/catalyst is controlled based on the estimated temperature. In this conventional technology, an estimated catalyst temperature Tc is computed by the following equation from an exhaust gas temperature Tg1 at the inlet of the filter/catalyst, and an exhaust gas temperature Tg2 at the outlet of the filter/catalyst: Tc=p×Tg1+q×Tg2 (p and q are coefficients obtained from experiment).